Fungrim home page

Fungrim entry: 209fc8

(zk+1)=z−kk+1(zk){z \choose k + 1} = \frac{z - k}{k + 1} {z \choose k}
Assumptions:z∈C and⁡ k∈Z≥0z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}
TeX:
{z \choose k + 1} = \frac{z - k}{k + 1} {z \choose k}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Binomial(nk){n \choose k} Binomial coefficient
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("209fc8"),
    Formula(Equal(Binomial(z, Add(k, 1)), Mul(Div(Sub(z, k), Add(k, 1)), Binomial(z, k)))),
    Variables(z, k),
    Assumptions(And(Element(z, CC), Element(k, ZZGreaterEqual(0)))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC